Characteristic X Rays and Auger Electrons

Interaction of Charged Particles with Matter

When charged particles pass through matter, they interact with the atomic electrons and lose energy through the processes of excitation and ionization. Ionization can also be produced when photons pass through matter via interactions such as the photoelectric effect and incoherent scattering. Excitation occurs when some of the incident particle's energy is transferred to the electron in the material, displacing it to higher energy shells (further from the nucleus), leaving a vacancy in the original shell.

If the energy transferred is sufficient to overcome the binding energy of the electron, ionization occurs, resulting in the ejection of the electron from the atom, forming an ion pair—an ejected electron and a positively charged ion. For instance, the binding energies for carbon, nitrogen, and oxygen are approximately 11.3 eV, 14.5 eV, and 13.6 eV, respectively. The average energy required to produce an ion pair in dry air (mostly nitrogen and oxygen) is 33.97 eV.

Creation of Vacancies and Energy Release

When a vacancy is created in an inner shell (due to excitation or ionization), it is filled by an electron from a higher shell. This process cascades as more vacancies are created, with each transition releasing energy either as electromagnetic radiation (X-rays) or by the ejection of an electron (Auger electron). The emitted X-rays are characteristic of the atom and are known as characteristic or fluorescent X-rays.

Fluorescent X-rays and Auger Electrons

The X-rays emitted during this process are called characteristic X-rays, as their energy is specific to the atom involved. The energy of the X-ray is equal to the difference in the binding energies of the electron shells involved in the transition. For example, X-rays resulting from transitions to the K-shell are called K characteristic X-rays, while those involving the L-shell are called L characteristic X-rays. The nomenclature is as follows:

• Kα X-ray: Emitted when an electron transitions from the L-shell to the K-shell.
• Kβ X-ray: Emitted when an electron transitions from the M or N shells to the K-shell.

Examples of Characteristic X-ray Energies (Tungsten)

For tungsten, the energies of the Kα and Kβ X-rays are given by the following equations:

Auger Electrons

If an Auger electron is emitted, the energy released by the transition is carried away by this electron, resulting in further vacancies in outer shells. For instance, when an electron transitions from the M-shell to the K-shell and an Auger electron is emitted from the M-shell, the kinetic energy of the Auger electron is given by:

Fluorescent Yield and Auger Electron Emission

The probability of emitting a fluorescent X-ray or an Auger electron is governed by the fluorescent yield (ω). The probability of emitting an Auger electron is \(1 - ω\). Auger electron emission is more significant for materials with low atomic numbers and for transitions involving outer shells. For example, the K fluorescence yield for different elements is as follows:

• Oxygen: 0.007
• Calcium: 0.17
• Selenium: 0.60
• Gadolinium: 0.93

Bremsstrahlung Radiation

In addition to characteristic X-rays and Auger electrons, accelerated electrons passing through matter can also produce bremsstrahlung radiation. This occurs when an electron is deflected by the nucleus, transferring energy to a photon. The photon energy can range from zero to the energy of the incident electron. Bremsstrahlung radiation contributes significantly to the X-ray spectrum emitted by X-ray tubes.

The probability of bremsstrahlung emission is proportional to the atomic number squared (\(Z^2\)), meaning that materials with higher atomic numbers, like tungsten (Z = 74), have a higher likelihood of bremsstrahlung production. However, the efficiency of bremsstrahlung production is still less than 1% for 100 keV electrons.